Neiman Marcus Group Ltd. is trying to remove the pain from growing online sales that trigger big, bulky items and high financial stakes for the retailer.

More shoppers are turning to online retailers for customized couches, new shelving or large appliances—items that can’t simply be dropped at the door by a mail or parcel carrier.

For Neiman, whose stores specialize in high-end home goods and designer furniture along with its other luxury brands, getting the goods to homes in a way that reflects the retailer’s high-end branding presents “continual challenges,” said Willis Weirich, the group’s senior vice president of supply chain and operations.

Of the thousands of “white glove” deliveries happening each month for Neiman Marcus and other retailers, at least one in 10 faces a delivery problem, such as an incorrect address or phone number, or a scheduling conflict with the carrier. That can reflect poorly on a company and slice profit margins for goods, and can end up costing a company future sales.

“We knew that we weren’t providing the customer experience that we’re so well-known for,” he told the Retail Industry Leaders Association’s Supply Chain conference this week. Often, the company didn’t even learn about a troubled delivery until after it had gone awry.

Mr. Weirich’s supply chain team collaborated with Neiman’s customer care group, using a cloud-based platform from Convey Software Inc. to track all of the retailer’s bulkiest, most complex deliveries to capture problems with enough time to correct them before the scheduled delivery date. Within 30 days of launching the software, Mr. Weirich said, Neiman Marcus had reduced its transit time to customers by 24%.

That means logistics companies that have been serving industrial business increasingly are tied to the consumer-facing side of retail. “The supply chain has more of an impact on the customer experience,” Mr. Weirich said.

Neiman investments in digital operations began to produce results late last year, when sales excluding newly opened or closed locations rose 4.2%, the first quarterly increase since 2015. About a third of Neiman’s $4.7 billion in annual sales comes from e-commerce, one sign that even wealthy shoppers now are searching online for the best deals.